Accelerated synthesis of neural network-based barrier certificates using collaborative learning

Most of existing Neural Network (NN)-based barrier certificate synthesis methods cannot deal with high-dimensional continuous systems, since a large quantity of sampled data may easily result in inaccurate initial models coupled with slow convergence rate. To accelerate the synthesis of NN-based barrier certificates, this paper presents an effective two-stage approach named CL-BC, which fully exploits the parallel processing capability of underlying hardware to enable quick search for a barrier certificate. Unlike existing NN-based methods that adopt a random initial model for barrier certificate synthesis, in the first stage CL-BC pre-trains an initial model based on a small subset of sampling data. In this way, an approximate barrier certificate in an NN form can be quickly achieved with little overhead. Based on our proposed collaborative learning scheme, in the second stage CL-BC conducts the parallel learning on partitioned domains, where the learned knowledge from different partitions can be aggregated to accelerate the convergence of a global NN model for barrier certificate synthesis. In this way, the overall synthesis time of an NN-based barrier certificate can be drastically reduced. Experimental results show that our approach can not only drastically reduce barrier synthesis time, but also can synthesize barrier certificates for complex systems that cannot be handled by state-of-the-art.